Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of a high-pressure inlet fogging method for a gas turbine engine. Exercise 12.19. Recall that you fit a first-order model for heat rate (y) as a function of speed (x1), inlet temperature (x2), exhaust temperature (x3), cycle pressure ratio (x4), and airflow rate (x5).
a. Researchers hypothesize that the linear relationship between heat rate (y) and temperature (both inlet and exhaust) depends on airflow rate. Write a model for heat rate that incorporates the researchers' theories.
b. Use statistical software to fit the interaction model, part a, to the data. Give the least squares prediction equation.
c. Conduct a test (at α = .05) to determine whether inlet temperature and airflow rate interact to affect heat rate.
d. Conduct a test (at α = .05) to determine whether exhaust temperature and airflow rate interact to affect heat rate.
e. Practically interpret the results of the tests, parts c and d.